Calculate linear momentum (p = mv), elastic and inelastic collisions, kinetic energy transfer, and conservation of momentum. Includes collision type reference.
Momentum — the product of mass and velocity — is one of the most fundamental conserved quantities in physics. In every collision, explosion, or interaction, total momentum is conserved regardless of the type of collision. Understanding momentum is essential for analyzing car crashes, rocket propulsion, particle physics, and sports impacts.
This Momentum Calculator operates in two modes: single-object momentum calculation and two-body collision analysis. For collisions, it handles both elastic (objects bounce) and perfectly inelastic (objects stick) types, computing post-collision velocities, kinetic energy before and after, and energy lost. The energy bar chart visualizes how much kinetic energy is conserved versus dissipated, and the reference table distinguishes collision types.
From physics homework to accident reconstruction, this calculator makes momentum conservation tangible with real-world presets and clear visualization of energy transfer. Check the example with realistic values before reporting. Use the steps shown to verify rounding and units. Cross-check this output using a known reference case.
Collision problems require solving simultaneous equations (momentum conservation and, for elastic collisions, energy conservation). This calculator solves them instantly, shows the energy budget visually, and handles the sign convention (negative velocity = opposite direction) that often trips up students. It is especially useful when you need to compare the before-and-after motion without rebuilding the algebra each time.
Momentum: p = mv Conservation: m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂' Elastic Collision: v₁' = [(m₁−m₂)v₁ + 2m₂v₂] / (m₁+m₂) v₂' = [(m₂−m₁)v₂ + 2m₁v₁] / (m₁+m₂) Perfectly Inelastic: v_f = (m₁v₁ + m₂v₂) / (m₁+m₂) Kinetic Energy: KE = ½mv²
Result: v_combined = 8.33 m/s, KE lost = 50%
A 1500 kg car at 60 km/h (16.67 m/s) rear-ending a stationary 1500 kg car in a perfectly inelastic collision results in both cars moving at 8.33 m/s (30 km/h). Half of the kinetic energy is lost to deformation and heat — demonstrating why crashes are so destructive.
Momentum conservation is one of the deepest principles in physics, arising from the translational symmetry of space (Noether's theorem). Unlike energy, which can change form, momentum is always conserved in a closed system — making it the most reliable tool for analyzing collisions and interactions.
Accident reconstruction engineers use momentum conservation to determine pre-collision speeds from post-collision evidence (skid marks, deformation, final positions). The equations are solved in both x and y directions for oblique (angled) collisions, and the coefficient of restitution is estimated from vehicle damage severity.
In particle accelerators, momentum conservation determines what products are possible in a collision and what angles they emerge at. Four-momentum (combining energy and 3D momentum into a relativistic four-vector) is the conserved quantity in special relativity, and its invariant mass is used to identify new particles.
By Newton's third law, internal forces between colliding objects are equal and opposite, so they cancel when summing momentum. External forces (gravity, friction) are negligible during brief collisions, so total momentum is conserved.
Elastic: both momentum and KE are conserved (objects bounce apart). Inelastic: momentum is conserved but KE is not — some converts to heat, sound, and deformation. Perfectly inelastic: objects stick together (maximum KE loss for a given momentum transfer).
In explosions (internal energy release), KE increases while momentum is still conserved. In ordinary collisions, KE either stays the same (elastic) or decreases (inelastic).
The coefficient of restitution e = (v₂' − v₁') / (v₁ − v₂) measures how "bouncy" a collision is. e = 1 is perfectly elastic, e = 0 is perfectly inelastic, and real collisions fall between.
Rockets use conservation of momentum: exhaust mass goes backward with high velocity, so the rocket gains forward momentum. The rocket equation (Tsiolkovsky) extends this to continuous mass ejection.
Angular momentum (L = Iω or L = r × p) is separately conserved in the absence of external torques. This calculator handles linear momentum only.